Fraction Classroom · 2.0.0 · Teacher answers & responses
Unit Fraction Builders: teaching companion
Name one equal part and connect repeated unit fractions to the whole. Student pages include two diagnostic probes, a reteaching check, and the original exit ticket. The teacher copy includes the complete lesson preparation, teaching sequence, diagnostic responses, all original question guides, and updated rubrics.
Complete lesson preparation
Grade 3 · 45 minutes. Build a whole by repeating a unit fraction.
materials. Materials: Pencil: 1 per student; Plain paper sheets: 2 per student; Projector: 1 per class (optional).
activity-1. Draw one strip. Make six equal sections and label one section 1/6.
activity-2. Cover the whole with six copies of that section. Repeat with thirds and fourths.
activity-3. Partners name the unit and explain how many copies make one whole.
phase-1. 5 min · warmup: Look at the first model or task. What is the whole? What do you notice?
Answer: Students: Sketch an initial prediction and explain it to a partner.
phase-2. 8 min · model: Draw one strip. Make six equal sections and label one section 1/6.
Answer: Students: Follow the model; label the whole and the equal parts.
phase-3. 10 min · partner: Cover the whole with six copies of that section. Repeat with thirds and fourths.
Answer: Students: Work in pairs. One models, the other checks; switch roles.
phase-4. 7 min · discussion: Partners name the unit and explain how many copies make one whole.
Answer: Students: Compare two solutions and explain the relationship.
phase-5. 10 min · practice: Choose core practice, or use the support prompts before moving to core. Use challenge prompts for explanation and transfer.
Answer: Students: Solve independently, then compare the reasoning.
phase-6. 5 min · exit: What is one part when a whole has four equal parts? Why do six copies of 1/6 make one whole?
Answer: Students: Complete the two exit questions independently.
Diagnostic probes
Explain or draw your reasoning. Your teacher will use these responses to choose what to revisit.
d1. One strip is split into six equal parts. Name one part, then say how many copies fill the strip.
Answer: One part is 1/6; six copies make 6/6 = 1.
Teacher response: If the learner names one part 1/5 by counting only the other pieces. Bracket all six pieces as one whole; touch the selected piece as well as the five others while counting the denominator.
d2. Build one whole with five 1/6 pieces. Is the whole complete?
Answer: No. It needs one more sixth.
Teacher response: If the learner treats five pieces as a whole because they form a connected strip. Keep the whole outline visible and compare the assembled pieces with the unfilled sixth.
Check after reteaching
Complete this check independently after discussing the model.
r1. A whole has eight equal parts. Name one part and the number of copies needed for the whole.
Answer: One part is 1/8; eight copies make one whole.
Exit ticket
Complete both original exit questions independently. Use a drawing or explanation when asked.
e1. What is one part when a whole has four equal parts?
Answer: 1/4
Teacher response: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole. Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
e2. Why do six copies of 1/6 make one whole?
Answer: Six copies cover all six equal parts exactly.
Look for:
- Name each copy as one of six equal parts.
- Account for all six copies with no gaps or overlap.
- Connect 6 × 1/6 or 6/6 with one whole.
Teacher response: Does not recognize that b copies of 1/b make one whole. Fill one outlined whole with b equal pieces and label the completed whole b/b. Exchange the complete collection for a card labeled 1; do the exchange again with a different partition.
Focused reteach
Name one equal part and connect repeated unit fractions to the whole.
teach-1. Draw a fixed whole with six equal slots and label one slot 1/6.
teach-2. Place one paper piece in each slot, counting sixths until 6/6.
teach-3. Repeat with fourths and ask why the number of copies changed while the whole stayed fixed.
Use the exit evidence
A wrong answer invites a follow-up probe; it does not by itself establish a particular misconception. Check e1 and e2 separately.
next-1. e1 meets its criterion: e1 gives 1/4 for one of four equal parts. e2 also meets its criterion: e2 explains that six sixths cover all six equal parts exactly.
Teacher response: Continue to the linked next lesson. Use the unit fraction as the piece size when counting several shaded pieces. Next original lesson: /lessons/fraction-strip-detective/.
next-2. e1 does not yet meet this criterion: e1 gives 1/4 for one of four equal parts.
Teacher response: Ask the learner to explain the attempt, then use the matching diagnostic probe to identify the difficulty. Work through the focused reteach below and its check. Use the linked short intervention if the difficulty persists; retry e1 and e2 before moving on. Short intervention: /interventions/denominator-size/.
next-3. e1 meets its criterion, but e2 does not yet show this evidence: e2 explains that six sixths cover all six equal parts exactly.
Teacher response: Ask the learner to assemble six 1/6 pieces inside a fixed outline, then describe why both the piece size and the count are needed. Short intervention: /interventions/denominator-size/.
Original question guide and updated rubrics
Use these question-specific teaching responses alongside the original lesson. Accept other mathematically valid open responses that meet the criteria. The original question wording and mathematical answers are retained; model descriptions below make their references readable offline.
c1. Six equal parts fill a whole. What is the value of one part? Strip model: 1 same-sized whole, each divided into 6 equal parts; 1 parts are shaded altogether.
Answer: 1/6
Teacher response: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole. Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
c2. Eight equal parts fill a whole. What is one part? Strip model: 1 same-sized whole, each divided into 8 equal parts; 1 parts are shaded altogether.
Answer: 1/8
Teacher response: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole. Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
c3. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 2 equal parts; 1 parts are shaded altogether.
Answer: 1/2
Teacher response: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole. Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
c4. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 3 equal parts; 1 parts are shaded altogether.
Answer: 1/3
Teacher response: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole. Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
c5. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 4 equal parts; 1 parts are shaded altogether.
Answer: 1/4
Teacher response: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole. Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
c6. How many copies of 1/4 fill one whole?
Answer: 4
Teacher response: Does not recognize that b copies of 1/b make one whole. Fill one outlined whole with b equal pieces and label the completed whole b/b. Exchange the complete collection for a card labeled 1; do the exchange again with a different partition.
c7. How many copies of 1/3 fill one whole?
Answer: 3
Teacher response: Does not recognize that b copies of 1/b make one whole. Fill one outlined whole with b equal pieces and label the completed whole b/b. Exchange the complete collection for a card labeled 1; do the exchange again with a different partition.
c8. What fraction do two copies of 1/6 cover? Strip model: 1 same-sized whole, each divided into 6 equal parts; 2 parts are shaded altogether.
Answer: 2/6
Teacher response: Reverses the shaded count and the total equal-part count. Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
s1. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 2 equal parts; 1 parts are shaded altogether.
Answer: 1/2
Teacher response: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole. Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
s2. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 3 equal parts; 1 parts are shaded altogether.
Answer: 1/3
Teacher response: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole. Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
s3. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 4 equal parts; 1 parts are shaded altogether.
Answer: 1/4
Teacher response: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole. Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
s4. What fraction is shaded? Write its value. Strip model: 1 same-sized whole, each divided into 6 equal parts; 1 parts are shaded altogether.
Answer: 1/6
Teacher response: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole. Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
h1. Explain why one sixth is smaller than one third of the same whole.
Answer: Sixths split the whole into more equal parts, so each is smaller.
Look for:
- Compare thirds and sixths of the same whole.
- Explain that six equal parts make smaller pieces than three equal parts.
- Conclude 1/6 < 1/3; a model showing two sixths in a third also supports the claim.
Teacher response: Assumes a larger denominator makes a larger piece when the whole and numerator are fixed. Fold identical strips into thirds and sixths. Place one third over two sixths, then compare one third with one sixth. For equal numerators, select the same number of pieces from each strip.
h2. Build 3/4 using only a 1/4 piece.
Answer: Repeat the quarter piece three times.
Look for:
- Use a 1/4 piece as the repeated unit.
- Show exactly three copies without gaps or overlaps.
- Label the result 3/4 of the original whole.
Teacher response: Reverses the shaded count and the total equal-part count. Use two labels: “equal pieces in one whole” under the bar and “pieces selected” above it. Point to every piece while naming the denominator, then only the selected pieces while naming the numerator.
h3. A child uses five sixths to build a whole. Repair the model.
Answer: Add one more sixth; six sixths are one whole.
Look for:
- Identify that five sixths leave one sixth uncovered.
- Add exactly one more 1/6 piece.
- State that 6/6 fills one whole.
Teacher response: Does not recognize that b copies of 1/b make one whole. Fill one outlined whole with b equal pieces and label the completed whole b/b. Exchange the complete collection for a card labeled 1; do the exchange again with a different partition.
h4. Invent two different unit-fraction tilings of one strip.
Answer: Two halves or four fourths each fill the same strip.
Look for:
- Give two distinct unit-fraction partitions, such as halves and fourths.
- Use equal-sized pieces within each partition.
- Show both sets filling the same strip exactly.
Teacher response: Does not recognize that b copies of 1/b make one whole. Fill one outlined whole with b equal pieces and label the completed whole b/b. Exchange the complete collection for a card labeled 1; do the exchange again with a different partition.
e1. What is one part when a whole has four equal parts?
Answer: 1/4
Teacher response: Treats the denominator as a count of selected pieces instead of the number of equal parts in one whole. Outline one whole first. Count all the equal pieces that fill it, label one piece 1/b, then repeat that piece until the whole is covered with no gaps.
e2. Why do six copies of 1/6 make one whole?
Answer: Six copies cover all six equal parts exactly.
Look for:
- Name each copy as one of six equal parts.
- Account for all six copies with no gaps or overlap.
- Connect 6 × 1/6 or 6/6 with one whole.
Teacher response: Does not recognize that b copies of 1/b make one whole. Fill one outlined whole with b equal pieces and label the completed whole b/b. Exchange the complete collection for a card labeled 1; do the exchange again with a different partition.
Teaching notes
- Teaching supplement version 2.0.0. Original lesson questions and PDF materials remain version 1.0.0. Original PDFs contain their original teaching notes and rubrics; use this supplement for the updated diagnostic guidance.
- Short intervention: /interventions/denominator-size/. Use its model for the identified difficulty, then return to this lesson’s check and exit ticket.
- Next original lesson: /lessons/fraction-strip-detective/. Use the unit fraction as the piece size when counting several shaded pieces.
- Open responses are reviewed by a teacher using the specific criteria. These materials have not been field-tested in classrooms.